A radio receiver has an effective resistance of 300 Ω to the input signal on the antenna downlead. The signal voltage is 700 µV. What is the signal current flow in the antenna downlead?

Answer:

1.81779 m/s in the same direction as the car

0.43220 m/s in the same direction

Explanation:

[tex]m_1[/tex] = Mass of van= 1055 kg

[tex]m_2[/tex] = Mass of car = 715 kg

[tex]u_1[/tex] = Initial Velocity of van = 0 m/s

[tex]u_2[/tex] = Initial Velocity of car = 2.25 m/s

[tex]v_1[/tex] = Final Velocity of van

[tex]v_2[/tex] = Final Velocity of car

As momentum and Energy is conserved

[tex]m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}[/tex]

[tex]{\tfrac {1}{2}}m_{1}u_{1}^{2}+{\tfrac {1}{2}}m_{2}u_{2}^{2}={\tfrac {1}{2}}m_{1}v_{1}^{2}+{\tfrac {1}{2}}m_{2}v_{2}^{2}[/tex]

From the two equations we get

[tex]v_{1}=\dfrac{m_1-m_2}{m_1+m_2}u_{1}+\dfrac{2m_2}{m_1+m_2}u_2\\\Rightarrow v_1=\dfrac{1055-715}{1055+715}\times 0+\dfrac{2\times 715}{1055+715}\times 2.25\\\Rightarrow v_1=1.81779\ m/s[/tex]

The final velocity of the van is 1.81779 m/s in the same direction as the car

[tex]v_{2}=\dfrac{2m_1}{m_1+m_2}u_{1}+\dfrac{m_2-m_1}{m_1+m_2}u_2\\\Rightarrow v_2=\dfrac{2\times 1055}{1055+715}\times 0+\dfrac{1055-715}{1055+715}\times 2.25\\\Rightarrow v_2=0.43220\ m/s[/tex]

The final velocity of the car is 0.43220 m/s in the same direction

Answer:

(a). The final velocity of the car is -0.432 m/s.

(b). The final velocity of the van is 1.82 m/s.

Explanation:

Given that,

Mass of van = 1055 kg

Mass of car = 715 kg

Initial velocity of car= 2.25 m/s

(a). We need to calculate the final velocity of the car

Using formula of velocity

[tex]v_{c}=\dfrac{m_{v}-m_{c}}{m_{v}+m_{c}}\times u_{c}[/tex]

Put the value into the formula

[tex]v_{c}=\dfrac{715-1055}{715+1055}\times2.25[/tex]

[tex]v_{c}=-0.432\ m/s[/tex]

(b). We need to calculate the final velocity of the van

Using formula of velocity

[tex]v_{v}=\dfrac{2m_{v}}{m_{v}+m_{c}}\times u_{c}[/tex]

Put the value into the formula

[tex]v_{v}=\dfrac{2\times715}{715+1055}\times2.25[/tex]

[tex]v_{v}=1.82\ m/s[/tex]

Hence, (a). The final velocity of the car is -0.432 m/s.

(b). The final velocity of the van is 1.82 m/s.

Answer:

D. Graphing the force as a function of distance and calculating the area under the curve.

Explanation:

Answer:

The correct option is (D). "Graphing the force as a function of distance and calculating the area under the curve"

Explanation:

1) As we know from the definition of Work done which is Work = Force × Displacement. Time doesn't have any use in the mentioned equation and thus the stop watch is of no use to us.

2) Using the meter stick, we can measure the distance for which the block is pulled horizontally i.e "Displacement"

3) Using the spring scale, we can calculate the "Force" applied on the block of wood to move it horizontally.

4) For example, lets say that for a constant force of 4 Newtons, the wooden block is pulled horizontally 4 meters. Plotting Force vs Displacement on a graph would yield a horizontal line as shown in the attachment. Area under the F vs D graph will give us the total work done.

Torque can cause the angular momentum vector to rotate in UCM. This motion is called _Conservation of Angular momentum__________.

Answer:

Conservation of Angular momentum

Explanation:

The motion of an object in a circular path at constant speed is known as uniform circular motion (UCM). An object in UCM is constantly changing direction, and since velocity is a vector and has direction, you could say that an object undergoing UCM has a constantly changing velocity, even if its speed remains constant.

The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.

Key Points

When an object is spinning in a closed system and no external torques are applied to it, it will have no change in angular momentum.

The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation.

If the net torque is zero, then angular momentum is constant or conserved.

Angular Momentum

The conserved quantity we are investigating is called angular momentum. The symbol for angular momentum is the letter L. Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero. We can see this by considering Newton’s 2nd law for rotational motion:

τ→=dL→dt, where  

τ is the torque. For the situation in which the net torque is zero,  

dL→dt=0.

If the change in angular momentum ΔL is zero, then the angular momentum is constant; therefore,

⇒

L  =constant

L=constant (when net τ=0).

This is an expression for the law of conservation of angular momentum.

Example and Implications

An example of conservation of angular momentum is seen in an ice skater executing a spin,  The net torque on her is very close to zero,

because (1) there is relatively little friction between her skates and the ice, and (2) the friction is exerted very close to the pivot point.

Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum. These laws are applicable even in microscopic domains where quantum mechanics governs; they exist due to inherent symmetries present in nature.

Precession is the rotation of the angular momentum vector in uniform circular motion (UCM) caused by torque. Torque's direction aligns with the direction of the angular momentum it produces. Any alteration in angular momentum is influenced by the average torque and the time period of its exertion, adhering to the conservation laws of angular momentum.

The motion caused by torque making the angular momentum vector to rotate in UCM is called precession. In other words, precession is the circular motion of the pole of the axis of a spinning object around another axis due to torque. This is similar to how a spinning top wobbles as it continues to spin.

For example, if we consider a merry-go-round, torque is perpendicular to the plane formed by radius and force. This direction aligns with the direction your right thumb would point to if you curled your fingers in the direction of the force. This shows that the direction of the torque is the same as that of the angular momentum it produces.

It's important to note that angular momentum, like energy and linear momentum, is conserved when the net external torque is zero. This is a universally applicable law underlying unity in physical laws. The change in angular momentum is given by the product of average torque and the time interval during which the torque is exerted, embodying the conservation laws of angular momentum.

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The question is asking for the distance an object will travel given its initial speed and a coefficient of friction. However, without knowing the object's mass, we cannot calculate the exact distance.

The question is asking you to calculate the distance an object will travel, given an initial speed and friction. This is a physics problem that can be solved using the principles of friction and kinetic energy.

Since we know the coefficient of kinetic friction (μk) and initial speed (v), we can calculate the distance travelled. The frictional force is equal to μk * m * g, where m is the mass of the object and g is the gravity. However, we do not have the mass of the object.

As we have incomplete information provided in the question, we cannot calculate the exact distance travelled. The chapter references given also do not give us the necessary information to solve the problem. With full information, we would use the formula relating kinetic energy to work done by friction to find the distance:

1/2 * m * v² = μk * m * g * d,  which simplifies to d = v² / (2 * g * μk)

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Answer:

a)W = 116800 J

b)KE=132496 J

c)P=4154.93 W

Explanation:

Given that

m= 800 kg/min

h= 14.6 m

v= 18.2 m/s

a)

Work done required ,W= m g h

h=height of the well

m=mass

W= 800 x 14.6 x 10                 ( take g= 10 m/s²)

W = 116800 J

b)

kinetic energy = KE

[tex]KE=\dfrac{1}{2}mv^2[/tex]

m=mass

v=velocity

[tex]KE=\dfrac{1}{2}\times 800\times 18.2^2[/tex]

KE=132496 J

c)

Pump power given as

[tex]P=\dfrac{W'}{t}[/tex]

W'=Total work done

t=time

[tex]P=\dfrac{116800+132496}{60}[/tex]

P=4154.93 W

The work done per minute in lifting the water is 114,464 J. The kinetic energy given to the water when it is ejected is 132,488 J. The power output of the pump is 4116.2 W.

The subject of this question is Physics, specifically the topic of work, energy, and power.

To calculate the work done in lifting the water, we can use the formula:

Work = Force × Distance

The force required to lift the water can be calculated using the formula:

Force = Mass × Gravity

(a) To find the work done per minute in lifting the water, we multiply the weight of the water by the height it is lifted. The weight of the water is mass times gravity, which is

Force =800 kg * 9.8 m/s^2 = 7840 N.

So, the work done is 7840 N * 14.6 m = 114,464 J.

(b) To find the kinetic energy given to the water when it is ejected, we use the formula for kinetic energy, which is 1/2 * mass * speed^2.

So, the kinetic energy = 1/2 * 800 kg * (18.2 m/s)^2

                                     = 132,488 J.

(c) The power output of the pump is the total work done per minute divided by the time, which is

Power =(114,464 J + 132,488 J) / 60 s

           = 4116.2 W.

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Answer:C. 10N

Explanation:

The applied force needed to maintain a constant velocity is 10N. This is because the moving force acting on the body will always be equal to the frictional force if the velocity of the body is constant.

But note that this is not the case if the body ia accelerating. If the body is accelerating then the frictional force will not be able to overcome the moving force acting on the body and such the moving force will be greater than the frictional force in that regards.

The applied force needed to maintain a constant velocity is 10 N.

The given parameters;

The net horizontal force on the object is calculated by applying Newton's second law of motion as shown below;

∑F = ma

[tex]F- F_k = ma[/tex]

where;

At constant velocity, the acceleration of the object is zero.

[tex]F-F_k = m(0)\\\\F-F_k = 0\\\\F= F_k\\\\F = 10 \ N[/tex]

Thus, the applied force needed to maintain a constant velocity is 10 N.

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Answer:

I = 1.21x10^-5 A

Explanation:

You are missing the first part of the problem. This is an example, but it will give you the idea of how to solve yours with your data.

The first part is like this:

A      4.0 cm  diameter parallel plate capacitor has a  0.44 m  m    gap. What is the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500,000 V/s?

Now with this, we can solve the problem.

In order to do this, we need to use the following expression:

q = CV (1)

Where:

C: Capacitance of a parellel capacitor (in Faraday)

q: charge of plate or capacitor (In coulombs)

V: voltage in Volts.

However, we need is the current, and we have data of potential difference, so, all we have to do is divide the expression between time so:

q/t = CV/t

And the current is q/t, thus:

I = C * V/t (2)

And finally, Capacitance C with two plates of area A separated by a distance d is:

C = Eo*A/d (3)

Where:

Eo = constant equals to 8.85x10^-12 F/m.

A = Area of the plate, in this case, πr²

d = gap of the capacitor.

Let's calculate first the Capacitance using equation (3):

C = 8.85x10^-12 * π * (0.04/2)² / 0.00046 = 2.42x10^-11 F

Now, it's time to use equation (2) and solve for I:

I = 2.42x10^-11 * 500,000

I = 1.21x10^-5 A

Answer:

The number of bright fringes per unit width on the screen is, [tex]x=\dfrac{\lambda D}{d}[/tex]      

Explanation:

If d is the separation between slits, D is the distance between the slit and the screen and [tex]\lambda[/tex] is the wavelength of the light. Let x is the  number of bright fringes per unit width on the screen is given by :

[tex]x=\dfrac{n\lambda D}{d}[/tex]

[tex]\lambda[/tex] is the wavelength

n is the order

If n = 1,

[tex]x=\dfrac{\lambda D}{d}[/tex]

So, the the number of bright fringes per unit width on the screen is [tex]\dfrac{\lambda D}{d}[/tex]. Hence, the correct option is (B).

Final answer:

The number of bright fringes per unit width in a Young's double-slit experiment is given by the reciprocal of the fringe spacing, which is d/(Dλ), corresponding to answer choice E.

Explanation:

In a Young's double-slit experiment, to find the number of bright fringes per unit width on the screen, we consider the separation between the slits (d), the distance from the slits to the screen (D), and the wavelength of light used (λ). The distance between adjacent bright fringes, or fringe spacing, is given by Δy = Dλ/d. From this relation, the number of bright fringes per unit width can be obtained by taking the reciprocal of the fringe spacing, which implies 1/Δy = d/(Dλ).

Therefore, the correct formula to calculate the number of bright fringes per unit width on the screen is the reciprocal of Δy, which is d/(Dλ), matching answer choice E.

Answer:

+ 3.0 m

Explanation:

displacement is shortest distance from fixed point O in particular direction . in diagram shortest distance at end from O is 3 m and it is right of O so +. HENCE +3.0m

Answer:

Electrolytes are considered ions when placed in a solution and allow for adequate conduction of particle charges.

Explanation:

Electrolytes are substances that, when are dissolved in solution, separates into electrical positive charges (cations) and electrical negative charges (anions) which are known as ions.

These ions have an adequate capacity to conduct particle charges and, therefore electricity.

Sodium, calcium, phosphate and potassium, are examples of electrolytes.  

Hence, the correct answer is:

Electrolytes are considered ions when placed in a solution and allow for adequate conduction of particle charges.

I hope it helps you!

Answer:

TRUE

Explanation:

It is TRUE that pedestrians, bicyclists and slow-moving vehicles are not allowed on expressways because expressways have minimum speed limit requirements that these travelers cannot reach. This minimum limit of speed varies country to country.

In America, the minimum speed limit in Rural Areas is 40 mph (miles per hour) i.e. 65km/h (kilometer per hour) while in Urban Areas it is 55mph i.e. 90km/h which cannot be met by pedestrians and by-cycles easily.

Answer:

d. 1000 N.

Explanation:

For the seesaw to be in equilibrium the moment on left of the fulcrum and the moment to the right of the fulcrum must be equal.

Let L be the distance on either side of fulcrum at which the boulder is kept

F be the minimum force used to pushdown the left end

According to principle

L×1000= L×F

F= 1000 N

Hence option D is correct

Answer:

False

Explanation:

A 24 year old motorcycle driver would not be required to wear protective eyewear when riding in Florida,This is a False statement.

The law is all riders would have to wear protective eyewear when riding in Florida.

Answer:

See below explanation

Explanation:

The correspondent chemical reaction for copper carbonate decomposed by heat is:

CuCO₃ (s) → CuO (s) + CO₂ (g)

Considering all molar mass (MM) for each element ( we consider rounded numbers) :

MM CuCO₃ = 123 g/mol

MM CuO = 79 g/mol

MM CO₂ = 44 g/mol

Statement mentions that scientis heated 123.6 g of CuCO₃ (almost a MM), until a black residue is obtained, which weights 79.6 g : this solid residue is formed by CuO, and the remaining mass (approximatelly 44 g) belongs to teh second product, this is, CO₂; as it is a gas compund, it is not certainly included on the solid residue.

So, law of conservation mass is true for this case, since: 123.6 g = 79.6 g + 44 g. As explained, on the solid residue, we don not include the 44 g, which  "escaped" from our system, since it is a gas compound (CO₂)

Based on the information given, it should be noted that the y component of the induced electric field will be E = -Bv.

An induced electric field simply means a nonconversative field that is generated due to a changing magnetic field.

The force that acts on the charge moving with the velocity is given. In this case, the component of the induced electric field will be E = -Bv.

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Answer:

a. Technician A

Explanation:

Technician A says that a MAF sensor is a high-authority sensor and is responsible for determining the fuel needs of the engine based on the measured amount of air entering the engine. Technician B says that a cold wire MAF sensor uses the electronics in the sensor itself to heat a wire 20°C below the temperature of the air entering the engine. Who is right

MAF wich stands for  mass airflow sensor determines the mass of air flowing into the engine's air intake system. ... , the wire cools When air flows past the wire, decreasing its resistance, thereby more current flows through the circuit. When the MAf goes bad, it can not sense the amount of air intake into the engine.

Answer:

u = 20.33 m/s

Explanation:

given,

mass of Toyota car = 950 Kg

mass of Cadillac = 2200 Kg

distance to stop = 4.8 m

coefficient of friction = 0.4

initial speed of the Toyota = ?

we know,

F = ma

and frictional foce

F = μ N = μ m g

where N is normal force

now equating both the equation

ma  = μ m g

 a = μ g

 a = 0.4 x 9.8

 a = 3.92 m/s²

using equation of motion

v² = u² + 2 a s

v² = 0² + 2 x 3.92 x 4.8

v = 6.13 m/s

above given velocity is the combined velocity of the Toyota and Cadillac

now, using conservation of momentum

m u = (M + m) v

950 x u = (2200+ 950) x 6.13

u = 20.33 m/s

The speed of Toyota before impact is equal to u = 20.33 m/s

Final answer:

The speed of the Toyota at the moment of impact is 0 m/s.

Explanation:

To find the speed of the Toyota at the moment of impact, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.

The momentum of an object is given by the product of its mass and velocity. So, we can write:

massT * velocityT = massC * velocityC

where massT and velocityT are the mass and velocity of the Toyota, and massC and velocityC are the mass and velocity of the Cadillac.

The mass of the Toyota is 950 kg, and the mass of the Cadillac is 2200 kg. The velocity of the Cadillac is 0 m/s because it is stopped. Solving for the velocity of the Toyota:

velocityT = (massC * velocityC) / massT

velocityT = (2200 kg * 0 m/s) / 950 kg = 0 m/s

Therefore, the speed of the Toyota at the moment of impact is 0 m/s.

Answer:3-Sonar

Explanation:

Sonar system is used to detect the under water objects by using the deflection of sound waves.

Sonar is an acronym of Sound navigation ranging.Two types of sonar sets are used for working: active and passive. The active sonar system pushes out sound signals called pings, and then absorbs the return sound echo. Passive sound sets obtain sound echoes without transmitting their actual sound signals. Submarines are using sonar to track other vessels.    

Answer:

T=2.94*10^-10  N/m.

Explanation:

Biologists think that some spiders "tune" strands of their web to give enhanced response at frequencies corresponding to those at which desirable prey might struggle. Orb spider web silk has a typical diameter of 20μm, and spider silk has a density of 1300 kg/m³.

To have a fundamental frequency at 150Hz , to what tension must a spider adjust a 14cm -long strand of silk?

l=length of the spider silk, 14cm

velocity of wave = √(T/μ)          

where T = tension and

μ = mass per unit length)

λ/2=l

for fundamental frequency λ/2 =14cm    

 (λ= wavelength of standing wave;  as there will be no node

   except the endpoints of silk strand)

               λ = 28 cm = 0.28 m

and since frequency * wavelength = speed of wave. we have,

                  150 * 0.28 = √(T/μ)                                        ..................(#)

now μ = mass/length = [volume * density]/length = [(length*area) * density] / length = area * density

         = [π * (10 * 10^(-6))²] * 1300  = 13π * 10^(-8).

now putting this in equation (#) we get

    150 * 0.28 = √(T/[13π * 10^(-8)]).

thus T = [13π * 10^(-8)] * (42)²     =  

2.94*10^-10  N/m.

Explanation:

The infographic lacks a possible solution to the issue, but it does explain where plastics emerge from, how they get into the marine, what they will do to marine wildlife, and how they will be removed to eliminate ocean plastic waste.

According to estimates reported in 2015 in the journal Science, between 4.8 million and 12.7 million tons of plastic enter the ocean every year. As large, identifiable items or as micro plastics, plastic can enter the ocean-pieces of less than five millimeters in length.

Answer:

The height at which the ladder safely reach on the garage is 12 meters.

Explanation:

It is given that,

Height of the ladder, H = 13 foot

Bottom of the ladder, B = 5 feet

To find,

How high can the ladder safely reach on the garage?

Solution,

The ladder and the wall follows the Pythagoras theorem. 13 foot is the height of the ladder. Distance between wall and the ladder is 5 feet. Let L is the height at which the ladder safely reach on the garage. On using Pythagoras theorem we get :

[tex]H^2=B^2+L^2[/tex]

[tex]L^2=H^2-B^2[/tex]

[tex]L^2=13^2-5^2[/tex]

L = 12 m

So, the height at which the ladder safely reach on the garage is 12 meters. Hence, this is the required solution.

Answer:

a. P1=200235pa

b. h=26.91m

Explanation:

The main water line enters a house on the first floor. The line has a gauge pressure of 2.64 x 105 Pa.

(a) A faucet on the second floor, 6.50 m above the first floor is turned off. What is the gauge pressure at this faucet?

(b) How high could a faucet be before no water would flow from it, even if the faucet were open?

pressure is the force per unit area.

force is that which tends to change a boy's state of rest or uniform motion in a straight line

rho stands for the density of water which is 1000kg/m3

p2=p1+rhogh

p1=p2-rhogh

the gauge pressure at 6.5m

will be:

2.64 x 10^5 Pa-100kg/m3*9.81*6.5

P1=200235pa

b. How high could a faucet be before no water would flow from it, even if the faucet were open?

b.h=p2-p1/(grho)

h=2.64 x 105 Pa/(1000*9.81)

h=26.91m

To find the gauge pressure and height limit of a faucet on the second floor compared to the first floor in a house with a main water line.

(a) To find the gauge pressure at the faucet on the second floor, we can use the equation: P2 = P1 + ρgh. Here, P1 = 2.64 x 105 Pa, ρ is the density of water, g is the acceleration due to gravity, and h is the height difference between the first and second floor. Plugging in the values, we get: P2 = 2.64 x 105 + (1000 kg/m3) x (9.8 m/s2) x 6.50 m. Solving for P2 gives us the gauge pressure at the faucet on the second floor.

(b) To find the maximum height a faucet could be before no water would flow from it, we can equate the gauge pressure to zero in the equation: P2 = P1 + ρgh. Solving for h, we can find the maximum height.

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Answer:

[tex]v_{f}[/tex] = 0  miles/h

Explanation:

This exercise should be resolved with the moment. The system is formed by the two cars. Let's write the moment

Initial. Before the crash

           p₀ = m v₁ - m v₂

The sign is because they go in the opposite direction

Final. After the crash

          [tex]p_{f}[/tex] = (m + m) [tex]v_{f}[/tex]

The moment is preserved

         p₀ = [tex]p_{f}[/tex]

         m v₁- m v₂ = 2m [tex]v_{f}[/tex]

         [tex]v_{f}[/tex] = m / 2m (v₁-v₂)

But the speed of the cars is the same v1 = v2 = 50 liters / h

       [tex]v_{f}[/tex] = 0

so the two faces do not move after the crash

Answer:

When flying the LNAV Approach, the missed approach point (MAP) would be indicated by reaching:

C. the RW30 waypoint.

Explanation:

The missed approach point (MAP) during an LNAV approach is indicated by reaching the RW30 waypoint.

When flying the LNAV approach, the missed approach point (MAP) would be indicated by reaching the RW30 waypoint. During an LNAV approach, which is a type of non-precision instrument approach procedure, pilots use lateral navigation to align with the runway. The MAP is typically defined by a waypoint and not by reaching a particular altitude or distance to the runway. Unlike precision approaches that can bring an aircraft to a lower minimum descent altitude or decision height based on a glideslope, LNAV approaches only provide lateral guidance and rely on predetermined waypoints to establish the MAP.

Answer:

d) An object that is speeding up always has a positive acceleration, regardless of the direction it travels.

Explanation:

a ) a) An object that is slowing down while traveling in the negative x-direction always has a positive acceleration.

It has negative acceleration in  the negative x-direction.

b) An object that is speeding up while traveling in the negative x-direction always has a positive acceleration.

It has a positive acceleration in the negative x-direction'

c) An object that is slowing down always has a negative acceleration, regardless of the direction it travels.

It has a positive  acceleration in opposite direction.

e ) An object that is slowing down always has a positive acceleration, regardless of the direction it travels.

It has a positive acceleration only in opposite direction .

Answer:

B. Wave-like way with a pattern that is wave-like

Explanation:

The double slit experiment when performed with electromagnetic waves, gives a pattern of light lines and dark areas, equally spaced.

In the case of electrons we must use Broglie's duality principle that states that all things have the characteristics of particles and waves together. The characteristic observed in a given experiment depends on the type of experiment, using the relationship

          p = h /λ

Where p is the amount of motion of the particle and λ the wavelength associated with this particle

In consequence of the previous one to the screen it should arrive as a wave with a wave type pattern

Let's review the answer.

A) False. The pattern is wave type

B) True. The whole process is with undulating characteristics

C) False. A wave arrives

D) False. A wave arrives

Answer:

8m/s

Explanation:

The question is incomplete.

But if the given speed is 3m/s

t= 0.5s

From Newton's equation of motion v=u+at

U= 3m/s

V= 3+ 0.5×10 a=10m/s^2

v= 8m/s

Final answer:

The BASE jumper's speed after 0.5 seconds, with gravity approximated as 10 m/s², would be 5 m/s. This is calculated using kinematic equations in physics, which are not explicitly stated in the choices, therefore the correct answer is E) not given.

Explanation:

The subject of the question involves the principles of kinematics in physics. Given that we approximate the acceleration due to gravity (g) as 10 m/s², we can calculate the BASE jumper's speed after 0.5 seconds.

The formula to calculate the speed (v) of a falling object at a given time (t) when released from rest is v = gt. Therefore, after 0.5 seconds, the BASE jumper's speed would be v = 10 m/s² × 0.5 s = 5 m/s. None of the options A) 10 m/s, B) 8 m/s, C) 6 m/s, or D) 3 m/s exactly match this result. Hence, the correct answer is E) not given.

Answer:

B. [tex]V_{f}= 10\,cubic\,inches [/tex]

Explanation:

Assuming we are dealing with a perfect gas, we should use the perfect gas equation:

[tex]PV=nRT [/tex]

With T the temperature, V the volume, P the pressure, R the perfect gas constant and n the number of mol, we are going to use the subscripts i for the initial state when the gas has 20 cubic inches of volume and absolute pressure of 5 psi, and final state when the gas reaches 10 psi, so we have two equations:

[tex]P_{i}V_{i}=n_{i}RT_{i} [/tex] (1)

[tex] P_{f}V_{f}=n_{f}RT_{f}[/tex] (2)

Assuming the temperature and the number of moles remain constant (number of moles remain constant if we don't have a leak of gas) we should equate equations (1) and (2) because [tex] T_{i}=T_{f}[/tex], [tex]n_{i}=n_{f} [/tex] and R is an universal constant:

[tex]P_{i}V_{i}= P_{f}V_{f} [/tex], solving for [tex]V_{f} [/tex]

[tex]V_{f} =\frac{P_{i}V_{i}}{P_{f}} =\frac{(5)(20)}{10} [/tex]

[tex]V_{f}= 10 cubic\,inches [/tex]

The work done by air resistance on a skydiver with a constant velocity is -2.93 × 10⁵ J, as the air resistance force is equal but opposite to the gravitational force, and work is calculated as force times distance in the direction of the force.

The work done by a nonconservative force such as air resistance can be calculated as the product of the force and the distance over which it acts, in the direction of the force. Since the skydiver is falling with a constant velocity, the force of air resistance must be equal and opposite to the gravitational force acting on the skydiver, resulting in no net force and therefore no acceleration. The work done by air resistance is thus equal to the gravitational force times the distance fallen, with a negative sign because the force of air resistance acts in the opposite direction to the displacement.

First, we need to calculate the gravitational force acting on the skydiver:

F_gravity = mass × acceleration due to gravity

F_gravity = 92.0 kg × 9.8 m/s²

F_gravity = 901.6 N

Now, we can calculate the work done by air resistance:

Work = force × distance × cos(ϸ)

Since the angle (ϸ) between the force of air resistance and the direction of displacement is 180 degrees (opposite directions), cos(ϸ) is -1. Therefore:

Work = -901.6 N × 325 m × -1

Work = -2.93 × 10⁵ J

The correct answer is D) -2.93 times 10⁵ J, which means the work done by air resistance is negative because it acts in the direction opposite to the displacement.

Answer:

dr/dt = -2 cm/s.

Explanation:

The volume of a cone is given by:

[tex]V=\frac{1}{3} \pi r^{2}h[/tex] (1)

Let's take the derivative with respect to time in each side of (1).

[tex]\frac{dV}{dt}=\frac{1}{3} \pi \frac{d}{dt}(r^{2}h)=\frac{1}{3} \pi \left(2r\frac{dr}{dt}h+r^{2}\frac{dh}{dt} \right)[/tex] (2)

We know that:

We can calculate how fast is the radius changing using the above information.

[tex]0=\frac{1}{3} \pi \left( 2\cdot 4\cdot \frac{dr}{dt} \cdot 10 + 4^{2}\cdot 10)\right[/tex]  

Therefore dr/dt will be:

[tex]\frac{dr}{dt}=-\frac{160}{80}=-2 cm/s[/tex]

The minus signs means that r is decreasing.

I hope it helps you!